Shadowless
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Re: MX2 Integration Marathon
How do u get those integral symbols
How do u get those integral symbols
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HSC 2012-14 MX2 Integration Marathon (archive) (2 Viewers)
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rolpsy
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Re: MX2 Integration Marathon
yup
Now IIRC, that second integral is easily done by 2 applications of IBP and rearrangements.
D: i just realised its undefined at x = 0.. L'Hopital's rule?
SpiralFlex
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Re: MX2 Integration Marathon
ill have a go at ur soon! once i finish studying for mx1.
lol forgot to integrate, thank u, i fixed itlol you forgot to integrate!
which gives the correct answer
here is a really difficult one:
good luck
ill have a go at ur soon! once i finish studying for mx1.
seanieg89
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Re: MX2 Integration Marathon
U MAD BRO keep your integrals at the level of the MX2 integration topic. If you are interested in how to do these yourself, do outside research / ask in extracurricular. This thread is an inappropriate place to post them.
@Rolpsy nice question!
\,dx=\int_0^{\pi/2}(\pi/2-x)\tan(x)\,dx\\ \Rightarrow 2I=\int_0^{\pi/2}\frac{2x\cos^2(x)+2(\pi/2-x)\sin^2(x)}{2\sin(x)\cos(x)}\, dx\\=\int_0^{\pi/2}\frac{2x\cos(2x)+\frac{\pi}{2}(1-\cos(2x))}{\sin(2x)}\,dx\\\Rightarrow 4I=\int_0^{\pi}\frac{x\cos(x)+\frac{\pi}{2}(1-\cos(x))}{\sin(x)}\, dx\\=\int_0^{\pi/2}x\cot(x)\,dx+\frac{\pi}{2}\int_0^{\pi/2}\csc(x)-\cot(x)\,dx+\int_{\pi/2}^\pi (x-\pi)\cot(x)\,dx+\frac{\pi}{2}\int_{\pi/2}^\pi\csc(x)+\cot(x)\,dx\\=2I+\pi\int_0^{\pi/2}\csc(x)-\cot(x)\,dx\\=2I-\pi\log|1+\cos(x)|]^{\pi/2}_0\\\Rightarrow I=\frac{\pi}{2}\log(2).)
U MAD BRO keep your integrals at the level of the MX2 integration topic. If you are interested in how to do these yourself, do outside research / ask in extracurricular. This thread is an inappropriate place to post them.
@Rolpsy nice question!
Johnstan
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Re: MX2 Integration Marathon
best be getting involved brahFuuark this thread looks so interesting. Will get involved soon
Carrotsticks
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Re: MX2 Integration Marathon
You will never be asked straight out to evaluate special integrals like the Logarithmic, Sine, Gaussian Integrals all in one go. If anything, they will lead you into it.
You will never be asked straight out to evaluate special integrals like the Logarithmic, Sine, Gaussian Integrals all in one go. If anything, they will lead you into it.
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Carrotsticks
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Re: MX2 Integration Marathon
In which case, a Cauchy Principle Value is assigned.
But like seanieg89 said, try to keep your integrals relatively elementary in nature.
Sometimes, numerical values are assigned to integrals that would otherwise have no value because the domain of integration contains a point of singularity or a discontinuity.
In which case, a Cauchy Principle Value is assigned.
But like seanieg89 said, try to keep your integrals relatively elementary in nature.
Re: MX2 Integration Marathon
I'm really interested to know how to do these integrals, I'll post them in extracurricular =)
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